# An object is made of a prism with a spherical cap on its square shaped top. The cap's base has a diameter equal to the length of the top. The prism's height is  16 , the cap's height is 2 , and the cap's radius is 5 . What is the object's volume?

Aug 4, 2018

1097.37 cu. I would review my answer and improve and make corrections, if any. Please do not edit this answer.

#### Explanation:

From the dimensions of the spherical cap, the semi-angle that it

subtends at the center of its sphere,

$\alpha$ rad $= \arcsin \left(\frac{4}{5}\right) = 0.9273$,

The side length

of the square top of the prism is 2 (4 ) = 8.

The entire volume = Volume of the cap + volume of the prism

= (( volume of the cone + volume of the

spherical cap ) - volume of the cone) + volume of the prism

= ( 4/3 (5^3)alpha sin alpha - 1/3 pi (4^2)(3)) + (16)(8^2)

$= \frac{4}{3} \left({5}^{3}\right) \left(0.9273\right) \left(\frac{4}{5}\right) - \frac{1}{3} \left(3.1416\right) \left(9\right) \left(3\right)$

#= 1097.37 cu